File size: 8,713 Bytes
18be3e0
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
"""
BSD 3-Clause License
Copyright (c) 2017, Prem Seetharaman
All rights reserved.
* Redistribution and use in source and binary forms, with or without
  modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
  this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright notice, this
  list of conditions and the following disclaimer in the
  documentation and/or other materials provided with the distribution.
* Neither the name of the copyright holder nor the names of its
  contributors may be used to endorse or promote products derived from this
  software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
"""

import torch
import numpy as np
import torch.nn.functional as F
from torch.autograd import Variable
from scipy.signal import get_window
from librosa.util import pad_center, tiny
import librosa.util as librosa_util

def window_sumsquare(window, n_frames, hop_length=200, win_length=800,
                     n_fft=800, dtype=np.float32, norm=None):
    """
    # from librosa 0.6
    Compute the sum-square envelope of a window function at a given hop length.
    This is used to estimate modulation effects induced by windowing
    observations in short-time fourier transforms.
    Parameters
    ----------
    window : string, tuple, number, callable, or list-like
        Window specification, as in `get_window`
    n_frames : int > 0
        The number of analysis frames
    hop_length : int > 0
        The number of samples to advance between frames
    win_length : [optional]
        The length of the window function.  By default, this matches `n_fft`.
    n_fft : int > 0
        The length of each analysis frame.
    dtype : np.dtype
        The data type of the output
    Returns
    -------
    wss : np.ndarray, shape=`(n_fft + hop_length * (n_frames - 1))`
        The sum-squared envelope of the window function
    """
    if win_length is None:
        win_length = n_fft

    n = n_fft + hop_length * (n_frames - 1)
    x = np.zeros(n, dtype=dtype)

    # Compute the squared window at the desired length
    win_sq = get_window(window, win_length, fftbins=True)
    win_sq = librosa_util.normalize(win_sq, norm=norm)**2
    win_sq = librosa_util.pad_center(win_sq, n_fft)

    # Fill the envelope
    for i in range(n_frames):
        sample = i * hop_length
        x[sample:min(n, sample + n_fft)] += win_sq[:max(0, min(n_fft, n - sample))]
    return x


class STFT(torch.nn.Module):
    """adapted from Prem Seetharaman's https://github.com/pseeth/pytorch-stft"""
    def __init__(self, filter_length=800, hop_length=200, win_length=800,
                 window='hann'):
        super(STFT, self).__init__()
        self.filter_length = filter_length
        self.hop_length = hop_length
        self.win_length = win_length
        self.window = window
        self.forward_transform = None
        scale = self.filter_length / self.hop_length
        fourier_basis = np.fft.fft(np.eye(self.filter_length))

        cutoff = int((self.filter_length / 2 + 1))
        fourier_basis = np.vstack([np.real(fourier_basis[:cutoff, :]),
                                   np.imag(fourier_basis[:cutoff, :])])

        forward_basis = torch.FloatTensor(fourier_basis[:, None, :])
        inverse_basis = torch.FloatTensor(
            np.linalg.pinv(scale * fourier_basis).T[:, None, :])

        if window is not None:
            assert(filter_length >= win_length)
            # get window and zero center pad it to filter_length
            fft_window = get_window(window, win_length, fftbins=True)
            fft_window = pad_center(fft_window, filter_length)
            fft_window = torch.from_numpy(fft_window).float()

            # window the bases
            forward_basis *= fft_window
            inverse_basis *= fft_window

        self.register_buffer('forward_basis', forward_basis.float())
        self.register_buffer('inverse_basis', inverse_basis.float())

    def transform(self, input_data):
        num_batches = input_data.size(0)
        num_samples = input_data.size(1)

        self.num_samples = num_samples

        # similar to librosa, reflect-pad the input
        input_data = input_data.view(num_batches, 1, num_samples)
        input_data = F.pad(
            input_data.unsqueeze(1),
            (int(self.filter_length / 2), int(self.filter_length / 2), 0, 0),
            mode='reflect')
        input_data = input_data.squeeze(1)

        forward_transform = F.conv1d(
            input_data,
            Variable(self.forward_basis, requires_grad=False),
            stride=self.hop_length,
            padding=0)

        cutoff = int((self.filter_length / 2) + 1)
        real_part = forward_transform[:, :cutoff, :]
        imag_part = forward_transform[:, cutoff:, :]

        magnitude = torch.sqrt(real_part**2 + imag_part**2)
        phase = torch.autograd.Variable(
            torch.atan2(imag_part.data, real_part.data))

        return magnitude, phase

    def inverse(self, magnitude, phase):
        recombine_magnitude_phase = torch.cat(
            [magnitude*torch.cos(phase), magnitude*torch.sin(phase)], dim=1)

        inverse_transform = F.conv_transpose1d(
            recombine_magnitude_phase,
            Variable(self.inverse_basis, requires_grad=False),
            stride=self.hop_length,
            padding=0)

        if self.window is not None:
            window_sum = window_sumsquare(
                self.window, magnitude.size(-1), hop_length=self.hop_length,
                win_length=self.win_length, n_fft=self.filter_length,
                dtype=np.float32)
            # remove modulation effects
            approx_nonzero_indices = torch.from_numpy(
                np.where(window_sum > tiny(window_sum))[0])
            window_sum = torch.autograd.Variable(
                torch.from_numpy(window_sum), requires_grad=False)
            window_sum = window_sum.to(inverse_transform.device()) if magnitude.is_cuda else window_sum
            inverse_transform[:, :, approx_nonzero_indices] /= window_sum[approx_nonzero_indices]

            # scale by hop ratio
            inverse_transform *= float(self.filter_length) / self.hop_length

        inverse_transform = inverse_transform[:, :, int(self.filter_length/2):]
        inverse_transform = inverse_transform[:, :, :-int(self.filter_length/2):]

        return inverse_transform

    def forward(self, input_data):
        self.magnitude, self.phase = self.transform(input_data)
        reconstruction = self.inverse(self.magnitude, self.phase)
        return reconstruction


class TorchSTFT(torch.nn.Module):
    def __init__(self, filter_length=800, hop_length=200, win_length=800, window='hann'):
        super().__init__()
        self.filter_length = filter_length
        self.hop_length = hop_length
        self.win_length = win_length
        self.window = torch.from_numpy(get_window(window, win_length, fftbins=True).astype(np.float32))

    def transform(self, input_data):
        forward_transform = torch.stft(
            input_data,
            self.filter_length, self.hop_length, self.win_length, window=self.window.to(input_data.device),
            return_complex=True)

        return torch.abs(forward_transform), torch.angle(forward_transform)

    def inverse(self, magnitude, phase):
        inverse_transform = torch.istft(
            magnitude * torch.exp(phase * 1j),
            self.filter_length, self.hop_length, self.win_length, window=self.window.to(magnitude.device))

        return inverse_transform.unsqueeze(-2)  # unsqueeze to stay consistent with conv_transpose1d implementation

    def forward(self, input_data):
        self.magnitude, self.phase = self.transform(input_data)
        reconstruction = self.inverse(self.magnitude, self.phase)
        return reconstruction